I have created an annoucement app on a parent site. I would like to include this same app on the subsites. Is there an easy way to do this?
Apps (lists and and libraries) belong to the site or subsite that you create them in. You can think of a site or subsite as being like a folder that you use to group together related lists/libraries/pages and subsites (and they're a good way to manage access/permissions).
You can add another Announcements app to your subsite, but it would be a completely different Announcements app with it's own items.
If you want to just display the announcements from the parent site on the subsite, you can configure a web part on your subsite to display items from the announcements app on the parent site.
The best web part to use depends on the version of SharePoint you are using. For SharePoint 2007 or SharePoint 2010 it would probably be the Content Query Web Part (CQWP). For SharePoint 2013 or Online it would be either the Search Results Web Part or Content By Search Web Part.